The solution of `y^2dx+(x^2-xy+y^2)dy=0` is (A) `y=Ce^(tan^-1x)` (B) `y=Ce^(tan^-1y)` (C) `y=Ce^(tan^-1(y/x))` (D) `y=C[tan^-1(y/x)+e^(x^2)+y^2]`

The solution of the differential equation (1+y^2)+(x-e^(tan^-1y))dy/dx=0 is (A) x e^(2 tan^-1y)=e^(tan^-1y)+k (B) (x-2)=k e^(-tan^-1y) (C) x e^(tan^-1y)=e^(2 tan^-1y)+k (D) x e^(tan^-1y)=tan^-1y+k

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of the differential equation (1+y^2)+(xe^(tan^-1)y) (dy)/(dx)=0, is (1) (x-2)=ke^(tan^) -1y) (2) 2xe^(2tan^-1y) =e^(2tan^-1y)+k (3) xe^(tan^-1y)=tan^-1y+k (4) xe^(2tan ^-1y)=e^(tan^-1y)+k

The solution of x^2 dy/dx-xy=1+cos(y/x) is (A) tan(y/(2x))=C-1/(2x^2) (B) sec(y/x)=1+C/y (C) sin(y/x)=C+1/y (D) y^2=(C+x^2) tan(y/x)

Solution of differential equation (x^(2)+1)^(2)(dy)/(dx)+2x(x^(2)+1)y=1 is (A) y=(tan^(-1))/(x^(2)+1)+C( B) y=tan^(-1)x+C(C)y(x^(2)+1)=tan^(-1)x+C(D)y(tan^(-1)x)=x^(2)+C

If f(x) is differentiable, then the solution of dy+f\'(x)(y-f(x))dx=0 is (A) yf(x)=Ce^(-f(f(x))^2) (B) y+1=f(x)+Ce^(-f(x)) (C) f(x)=Cye^(-y^2/2) (D) none of these

y^(2)-(dy)/(dx)=x^(2)(dy)/(dx) A) y^(-1)+tan^(-1)x=c B) x^(-1)+tan^(-1)y=c C) y+tan^(-1)x=c D) x^(-1)+y^(-1)=tan^(-1)x+c

The solution of the equation dy/dx=x^3y^2+xy is (A) x^2y-2y+1=cye^(-x^2/2) (B) xy^2+2x-y=ce^(-y/2) (C) x^2y-2y+x=cxe^(-y/2) (D) none of these

The solution of differential equation (1+y^(2))+((x-2e^(tan^(-1)y))dy)/(dx)=0 is (x-2)=ke^(tan^(-1)y)xe^(tan-1)y=e^(2)tan^(-4)y+kxe^(tan^(-1)y)=tan^(-1)y+kxe^(2tan^(-1)y)=e^(2tan^(-1)y)+k

The integrating factor of (1 + y ^ 2) dx = (tan ^ (- 1) y - x) dy is (i) tan ^ (- 1) y (ii) tany (iii) e ^ (tan ^ (- 1) y) (iv) e ^ tany